Random walks on random lattices with traps

Abstract

A critical examination is presented of the continuous time random walk (CTRW) approximation and of frequency-dependent effective transition rate methods for calculating the configurational average of the Laplace transform of the probabilityPs, t|0) that a particle performing a random walk will be at site s timet after it reached the site s0. Some exact results are derived for the form of P(s, t|s0) at long times, and these indicate that the effective transition rate methods are the better approximation for systems with symmetric effective hopping rates, while the CTRW approximation is better for systems containing traps, i.e., states that are much easier to enter than to leave. The implications of these results for calculations of transient currents and of the ac conductivity for amorphous semiconductors are discussed.